In this paper, we introduce a method for estimating human left/right walking gait balance using footstep-induced structural vibrations. Understanding human gait balance is an integral component of assessing gait, neurological and musculoskeletal conditions, overall health status, and risk of falls. Existing techniques utilize pressure- sensing mats, wearable devices, and human observation-based assessment by healthcare providers. These existing methods are collectively limited in their operation and deployment; often requiring dense sensor deployment or direct user interaction. To address these limitations, we utilize footstep-induced structural vibration responses. Based on the physical insight that the vibration energy is a function of the force exerted by a footstep, we calculate the vibration signal energy due to a footstep and use it to estimate the footstep force. By comparing the footstep forces while walking, we determine balance. This approach enables non-intrusive gait balance assessment using sparsely deployed sensors. The primary research challenge is that the floor vibration signal energy is also significantly affected by the distance between the footstep location and the vibration sensor; this function is unclear in real-world scenarios and is a mixed function of wave propagation and structure-dependent properties. We overcome this challenge through footstep localization and incorporating structural factors into an analytical force-energy-distance function. This function is estimated through a nonlinear least squares regression analysis. We evaluate the performance of our method with a real-world deployment in a campus building. Our approach estimates footstep forces with a RMSE of 61.0N (8% of participant's body weight), representing a 1.54X improvement over the baseline.